A122968 -id:A122968 - cp's OEIS frontend

A137491 Numbers with 28 divisors.

960, 1344, 1728, 2112, 2240, 2496, 3264, 3520, 3648, 4160, 4416, 4928, 5440, 5568, 5824, 5832, 5952, 6080, 7104, 7290, 7360, 7616, 7872, 8000, 8256, 8512, 9024, 9152, 9280, 9920, 10176, 10206, 10304, 11328, 11712, 11840, 11968, 12864, 12992, 13120

Offset: 1

R. J. Mathar, Apr 22 2008

nonn

Maple implementation: see A030513.

Numbers of the form p^27 (subset of A122968), p*q^13, p*q*r^6 (A179672) or p^3*q^6 (A179694), where p, q and r are distinct primes. - R. J. Mathar, Mar 01 2010

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

with(numtheory): A137491:=n->`if`(tau(n)=28,n,NULL): seq(A137491(n), n=1..15000); # Wesley Ivan Hurt, Sep 18 2014

Select[Range[30000],DivisorSigma[0,#]==28&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

is(n)=numdiv(n)==28 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n)) = 28.

A122971 30th powers: a(n) = n^30.

Original entry on oeis.org

0, 1, 1073741824, 205891132094649, 1152921504606846976, 931322574615478515625, 221073919720733357899776, 22539340290692258087863249, 1237940039285380274899124224

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A122968, A122969, A122970.

Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers).

Range[0,10]^30 (* Harvey P. Dale, Mar 06 2019 *)

(A122971(n)=n^30); is_A122971(N)=ispower(N,30) \\ M. F. Hasler, Jul 24 2022

def A122971(n): return n**30
from sympy import nextprime
def is_A122971(N, k=30): # 2nd opt. arg to check for powers other than 30
    p = 2
    while N >= p**k:
        for e in range(N):
            if N % p: break
            N //= p
        if e % k: return False
        p = nextprime(p)
    return N < 2  #  M. F. Hasler, Jul 24 2022

Totally multiplicative sequence with a(p) = p^30 for prime p. Multiplicative sequence with a(p^e) = p^(30e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-30).
Sum_{n>=1} 1/a(n) = zeta(30) = 6892673020804*Pi^30/5660878804669082674070015625.
Sum_{n>=1} (-1)^(n+1)/a(n) = 536870911*zeta(30)/536870912 = 925118910976041358111*Pi^30/759790291646040068357842010112000000. (End)
Intersection of A000290 and A000578 and A000584. - M. F. Hasler, Jul 24 2022

A122969 28th powers: a(n) = n^28.

Original entry on oeis.org

0, 1, 268435456, 22876792454961, 72057594037927936, 37252902984619140625, 6140942214464815497216, 459986536544739960976801, 19342813113834066795298816, 523347633027360537213511521

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A010813, A089081, A122968.

Table[n^28,{n,0,16}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2010 *)
Range[0,16]^28 (* Harvey P. Dale, Dec 09 2012 *)

Totally multiplicative sequence with a(p) = p^28 for prime p. Multiplicative sequence with a(p^e) = p^(28e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-28).
Sum_{n>=1} 1/a(n) = zeta(28) = 6785560294*Pi^28/564653660170076273671875.
Sum_{n>=1} (-1)^(n+1)/a(n) = 134217727*zeta(28)/134217728 = 65053034220152267*Pi^28/5413323669636552217067520000000. (End)

A122970 29th powers: a(n) = n^29.

Original entry on oeis.org

0, 1, 536870912, 68630377364883, 288230376151711744, 186264514923095703125, 36845653286788892983296, 3219905755813179726837607, 154742504910672534362390528, 4710128697246244834921603689, 100000000000000000000000000000, 1586309297171491574414436704891

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

The least significant digit of a(n) is the same as the least significant digit of n. - Alonso del Arte, Mar 28 2015

Amiram Eldar, Table of n, a(n) for n = 0..10000
Index to divisibility sequences

Cf. A089081, A122968, A122969.

[n^29: n in [0..10]]; // Vincenzo Librandi, Mar 29 2015

Range[0, 9]^29 (* Alonso del Arte, Mar 28 2015 *)

a(n)=n^29 \\ Charles R Greathouse IV, Jun 28 2015

Completely multiplicative sequence with a(p) = p^29 for prime p. Multiplicative sequence with a(p^e) = p^(29e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-29).
Sum_{n>=1} 1/a(n) = zeta(29).
Sum_{n>=1} (-1)^(n+1)/a(n) = 268435455*zeta(29)/268435456. (End)

a(10)-a(11) from Michel Marcus, Mar 29 2015

A194561 Centered cube numbers: (n+1)^27 + n^27.

Original entry on oeis.org

1, 134217729, 7625731702715, 18022024106966971, 7468594995433310109, 1030940949674393077661, 66735852732611749389079, 2483564001592792629551895, 60567588642269318039802521, 1058149737003040059690390169, 14109994191499930367061460371

Offset: 0

Jonathan Vos Post, Aug 28 2011

These are the lowest dimension of k-dimensional centered cube numbers which not only cannot be prime, but which, after the trivial a(0), always have at least 4 prime factors, because a(n) = (2n + 1) * (n^2 + n + 1) * (n^6 + 3n^5 + 12n^4 + 19n^3 + 15n^2 + 6n + 1) * (n^18 + 9n^17 + 117n^16 + 732n^15 + 2934n^14 + 8442n^13 + 18480n^12 + 31788n^11 + 43749n^10 + 48619n^9 + 43758n^8 + 31824n^7 + 18564n^6 + 8568n^5 + 3060n^4 + 816n^3 + 153n^2 + 18n + 1).

			The minimum nontrivial number of prime factors first appears at a(2) = 7625731702715 = 5 * 7 * 577 * 377604937.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A122968, A194553.

[(n+1)^27+n^27: n in [0..10]]; // Vincenzo Librandi, Sep 21 2011

a(n)=(n+1)^27+n^27; \\ Andrew Howroyd, Feb 05 2018

a(8)-a(10) from Andrew Howroyd, Feb 05 2018

cp's OEIS Frontend

A137491 Numbers with 28 divisors.

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A122971 30th powers: a(n) = n^30.

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A122969 28th powers: a(n) = n^28.

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A122970 29th powers: a(n) = n^29.

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A194561 Centered cube numbers: (n+1)^27 + n^27.

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